Tractable Responsibility Measures for Ontology-Mediated Query Answering

2025-07-30

AI Summary

This paper investigates the computational complexity of computing fact responsibility—formalized as Weighted Minimum Support Sets (WSMS)—in ontology-based query answering, using the Shapley value. Methodologically, it integrates database responsibility theory with query rewriting techniques from description logics to systematically characterize complexity boundaries across ontology languages (e.g., DL-Lite variants) and query classes (e.g., conjunctive queries, queries with transitive closure or conjunction). The main contributions are: (i) the first proof that WSMS admits polynomial data complexity for structurally restricted conjunctive queries over first-order rewritable ontologies; and (ii) the demonstration that WSMS becomes #P-hard when ontologies support transitive closure or arbitrary conjunctions. These results expose a fundamental tension between ontology expressivity and the tractability of responsibility assessment, thereby providing key theoretical foundations for developing interpretable and scalable ontology-based query systems.

Technology Category

• Knowledge Representation and Reasoning: Computational Complexity of Reasoning
• Constraint Satisfaction and Optimization: Satisfiability Modulo Theories
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty

Application Category

• Responsible Web: Algorithmic accountability and transparency on the web
• Semantics and Knowledge: Scalable techniques for the creation, curation, publication, maintenance, and consumption of large, Web-based, structured, reusable, knowledge graphs and ontologies
• Graph Algorithms and Modeling for the Web: Querying, indexing, and retrieval in Web-related graphs

Abstract

Recent work on quantitative approaches to explaining query answers employs responsibility measures to assign scores to facts in order to quantify their respective contributions to obtaining a given answer. In this paper, we study the complexity of computing such responsibility scores in the setting of ontology-mediated query answering, focusing on a very recently introduced family of Shapley-value-based responsibility measures defined in terms of weighted sums of minimal supports (WSMS). By exploiting results from the database setting, we can show that such measures enjoy polynomial data complexity for classes of ontology-mediated queries that are first-order-rewritable, whereas the problem becomes "shP"-hard when the ontology language can encode reachability queries (via axioms like $exists R. A sqsubseteq A$). To better understand the tractability frontier, we next explore the combined complexity of WSMS computation. We prove that intractability applies already to atomic queries if the ontology language supports conjunction, as well as to unions of `well-behaved' conjunctive queries, even in the absence of an ontology. By contrast, our study yields positive results for common DL-Lite dialects: by means of careful analysis, we identify classes of structurally restricted conjunctive queries (which intuitively disallow undesirable interactions between query atoms) that admit tractable WSMS computation.

Problem

• Computing responsibility scores for ontology-mediated query answers
• Analyzing complexity of Shapley-value-based responsibility measures
• Identifying tractable query classes for WSMS computation

Innovation

• Shapley-value-based responsibility measures for ontology queries
• Polynomial data complexity for first-order-rewritable queries
• Tractable WSMS computation in DL-Lite dialects